Second order methods for open loop optimal control problems governed by the two-dimensional instationary-Navier Stokes equations are investigated. Optimality systems based on a Lagrangian formulation and adjoint equations are derived. The Newton and quasi-Newton methods as well as various variants of SQP methods are developed for applications to optimal ow control, and their complexity in terms of system solves is discussed. Local convergence and rate of convergence are proved. A numerical example illustrates the feasibility of solving optimal control problems for two-dimensional instationary Navier-Stokes equations by second order numerical methods in a standard workstation environment.